"That's the only religion that we have," Cook said. "We must do something bold, something ambitious, something great for the customers, and we sweat all of the details."

In the meantime, customers and investors are waiting for Apple to do something bold and ambitious again, and Cook is calling out the competitors' products as wanting.

When questioned Tuesday during the second-quarter earnings call about Apple's stance on offering an iPhone with a 5-inch screen, he offered this revealing glimpse into his thinking:

My view continues to be that the iPhone 5 has the absolute best display in the industry. And we always strive to create the very best display for our customers. ... some customers value large screen size; others value also other factors such as resolution, color quality, white balance, brightness, reflectivity, screen longevity, power consumption, portability, compatibility with apps, and many things.

Our competitors had made some significant trade-offs in many of these areas in order to ship a larger display; we would not ship a larger display iPhone while these trade-offs exist.

The iPhone can get much brighter. This leads to punchier whites and better handling of bright ambient-light situations, particularly outdoors or under bright overhead lights.

The Galaxy S3 has much deeper black levels. The AMOLED screen of the Galaxy S3 can produce a much deeper, more realistic shade of black than the IPS (in-plane switching) LCD of the iPhone 5. This advantage shows up best under dim ambient-light conditions, such as outdoors at night or in a darker room.

Color on the iPhone is much more accurate. The iPhone hews significantly closer to the standard gamut used to produce most of the photos, videos, and other consumer content you'll view onscreen. That means it produces highly accurate colors. The Galaxy S3, on the other hand, has a gamut far beyond the standard, which oversaturates colors.

Samsung Galaxy S4
CNET

The Samsung Galaxy S4 screen may be a lot better. CNET reviewer Jessica Dolcourt wrote that the Galaxy S4's HD AMOLED display "nailed it with color saturation and contrast, sharply defined edges and details. Articles are easy to read, gameplay looks good, and photos and videos look terrific.

For mere mortals who aren't counting pixels, the Galaxy S4 screen achieves some excellence. It has issues with outdoor readability and is a bit dimmer than the competition, but as Dolcourt wrote, content looks from good to terrific on the 5-inch 1080p HD display with the stronger, thinner Gorilla Glass 3. (DisplayMate's Dr. Raymond M. Soneira recently published an in-depth technical comparison of the Galaxy S4 OLED screen and iPhone 5 LCD screen. Both were rated excellent.)

Cook seems to be willing to let others soak up the growing market for larger-sized smartphones for now. Good or terrific -- or even excellent -- doesn't seem to be enough for Apple. A larger iPhone must be as close to technical and artistic perfection as possible, and Apple will amaze people with punchier whites and color accuracy that most people cannot detect with the naked eye.

Apple sales have not fallen off a cliff, even without having a phone with a screen larger than 4 inches. The 3-year-old, low-cost iPhone 4, with a 3.5-inch screen, had strong sales in the quarter. The company sold 37.4 million iPhones in the first calendar quarter, compared to 35.1 million in the same period last year. But the outlook for the current quarter was underwhelming and may include a decline in revenue.

During the earnings call, Cook said that Apple would not have anything new to offer until the fall. A faster, lighter, and more clever iPhone 5 -- a 5S -- is the sequence that Apple followed with the iPhone 4, but my bet is that Apple also finally has found enough perfection and competitive need to bring a phone with 5-inch 1080p HD display to life.

This story has been updated to include DisplayMate's evaluation of the Galaxy S4 and iPhone 5 screens.